Area And Circumference of a Circle
Introduction
There are a number of important facts that you must know when it comes to the area and circumference of a circle.
- The edge or perimeter of a circle is referred to as the circumference
- A line passing from one end of a circle to another and which passes through the centre of the circle is its diameter.
- A line passing from one end of a circle to another and which does not pass through the centre of the circle is known as a chord.
- The diameter is twice the length of the radius.
- The formula for finding the circumference of a circle is given by: C=\pi d
- The formula for finding the area of a circle is given by: A=\pi r^2
Generally the value of \pi two decimal places is 3.14. You can use this or the button on your calculator.
Area And Circumference Of A Circle - Example 1
Example
Take a look at the following question:
You are asked to calculate the circumference where the formula is C=\pi d
The question only gives the radius so in order to find this diameter, this simply needs to be doubled. 6.1 ×2=12.2cm.
So C =3.14 ×12.2=38.308=38.3cm
Area And Circumference Of A Circle - Example 2
Example
Take a look at the following question:
Here you need to determine the perimeter and in order to do this the curved part of the shape needs to be determined. Clearly this is half a circle so the best method would be to find the circumference for a full circle and then to divide by two.
C=\pi d=3.14 \times 8=25.12 \mathrm{~cm}So the perimeter will be 25.12+10=35.12cm.
Area And Circumference Of A Circle – Example 3
Take a look at the following question:
Here you need to decide whether to work out the area or the circumference. The question does not actually say so you need to read the question carefully.
The third line has the words “side of the cake” so this must mean that it is referring to the circumference.
C = 3.14 x 7 = 22.19 inches
Next you need to convert this into cm’s so a multiplication needs to be performed: 22.19 x 2.54 = 56.36cm
Now because ribbon strips are sold in length’s of 50cm, one ribbon strip will not be enough.
Question Practice
Try the following question on your own before looking at the solution.
So how did you get on? Hopefully you got the correct answer of 175.84 \mathrm{~cm}^2
The question is asking about the area of the shaded region. There are three circles in total and you need to find the area of the two smaller circles and subtract this from the area of the larger circle.
You need to also be careful that for the smaller circles you are given the diameter so you need to halve this to obtain the radius.
Area of small circle = 3.14 \times 2^2=12.56 \mathrm{~cm}^2. The total area of the two smaller circles is 12.56 \times 2=25.12 \mathrm{~cm}^2
Area of large circle = 3.14 \times 8^2=200.96 \mathrm{~cm}^2
So the area of the shaded region = 200.96-25.12=175.84 \mathrm{~cm}^2
Questions regarding the area and circumference of a circle appear on both the foundation and higher paper. For the foundation paper obviously the questions will not be as challenging as those found on the higher paper. If you can understand and follow the examples in this article then you should be able to apply the skills learnt here to other questions.